Conductivity tensor of graphene dominated by spin-orbit coupling scatterers: A comparison between the results from Kubo and Boltzmann transport theories.
Conductivity tensor of graphene dominated by spin-orbit coupling scatterers: A comparison between the results from Kubo and Boltzmann transport theories.
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自旋轨道耦合散射体主导的石墨烯电导率张量：久保输运理论与玻尔兹曼输运理论结果的比较
DOI：
10.1038/srep23762
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发表时间：
2016-03-31
影响因子：
4.6
通讯作者：
Zheng Y
中科院分区：
文献类型：
--
作者：
Liu Z;Jiang L;Zheng Y
从理论上研究了自旋轨道耦合杂质散射引起的石墨烯的对角电导和霍尔电导。基于连续模型，即无质量狄拉克方程，我们从Kubo和Boltzmann输运理论导出了电导率张量的解析表达式。通过数值计算，我们发现在自洽玻恩近似下对角电导的Kubo量子输运结果在Dirac点附近存在一个绝缘能隙.在这个间隙中，出现了一个定义明确的量子化自旋霍尔平台。这表明石墨烯在自旋轨道耦合杂质的驱动下实现了量子自旋霍尔态。相比之下，半经典玻尔兹曼理论未能预测这样的拓扑绝缘相。即使在绝缘间隙中，玻尔兹曼对角电导率也不为零，其中玻尔兹曼自旋霍尔电导率不表现出任何量子化平台。
The diagonal and Hall conductivities of graphene arising from the spin-orbit coupling impurity scattering are theoretically studied. Based on the continuous model, i.e. the massless Dirac equation, we derive analytical expressions of the conductivity tensor from both the Kubo and Boltzmann transport theories. By performing numerical calculations, we find that the Kubo quantum transport result of the diagonal conductivity within the self-consistent Born approximation exhibits an insulating gap around the Dirac point. And in this gap a well-defined quantized spin Hall plateau occurs. This indicates the realization of the quantum spin Hall state of graphene driven by the spin-orbit coupling impurities. In contrast, the semi-classical Boltzmann theory fails to predict such a topological insulating phase. The Boltzmann diagonal conductivity is nonzero even in the insulating gap, in which the Boltzmann spin Hall conductivity does not exhibit any quantized plateau.